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Lecture
Number Theory: Division, Remainder, Congruence
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Related lectures (37)
Integers: Well Ordering and Induction
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Explores well ordering, induction, Euclidean division, and prime factorization in integers.
Euclidean Algorithm: GCD Calculation
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Covers the Euclidean algorithm for GCD calculation and algorithmic complexity analysis.
Cyclotomic Extensions: Norms, Ideals, and Primes
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Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.
Prime Gaps and Multiplicative Sieve Inequalities
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Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.
Algebraic Structures: Groups and Rings
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Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.
Primes in Arithmetic Progression
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Explores primes in arithmetic progression, focusing on L-functions, characters, and the divergence of the sum of 1 over p for p congruent to a modulo q.
Polynomial Factorization over a Field: Eigenvalues
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Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.
Algebraic Geometry: Rings and Bodies
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Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.
Function Composition and Integers
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Covers function composition and integers, including properties and examples.
Primes in arithmetic progressions (II), and Gamma functions
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Arithmetic functions
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Shor's factoring algorithm: Quantum Phase Estimation
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Covers Shor's factoring algorithm and the link between order finding and factoring.
Understanding Equivalence Relations and Integer Construction
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Covers the construction of integers through equivalence relations and their properties in mathematics.
Fermat's Equation: Integral Solutions and Gaussian Integers
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Discusses Fermat's equation and Gaussian integers' properties.
Field Properties: Irreducibility and Units
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Polynomials: Theory and Operations
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